Set-Theoretic Topology

George M. Reed

• Publisher: Academic Press
• Year: 2014
• Print ISBN: 9780125849500
• eBook ISBN: 9781483263922
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Set-Theoretic Topology deals with results concerning set theoretic topology and indicates directions for further investigations. Topics covered include normality and conditions in abstract spaces, compactifications, cardinal invariance, mapping theory, product spaces, and metrization. Comprised of 29 chapters, this volume begins with an example concerning the preservation of the Lindelöf property in product spaces, followed by a discussion on closed-completeness in spaces with a quasi-G? diagonal and with weak covering properties. The reader is then introduced to countably compact extensions of normal locally compact M-spaces; continuously semi-metrizable spaces; and closed discrete collections of singular cardinality. Subsequent chapters focus on open mapping theory; a selection-theoretic approach to certain extension theorems; semicompletable Moore spaces; and non-normal spaces. The book also considers complete mappings in base of countable order theory before concluding with an analysis of locally separable Moore spaces. This monograph should be of value to students, researchers, and specialists in the field of mathematics.

Table of contents

• Front Cover
• Set-Theoretic Topology
• Copyright Page
• Table of Contents
• Dedication
• CONTRIBUTORS
• PREFACE
• ACKNOWLEDGMENTS
• CHAPTER 1. AN EXAMPLE CONCERNING THE PRESERVATION OF THE LINDELÖF PROPERTY IN PRODUCT SPACES
• CHAPTER 2. CLOSED-COMPLETENESS IN SPACES WITH A QUASI-GδDIAGONAL
• CHAPTER 3. CLOSED-COMPLETENESS IN SPACES WITH WEAK COVERING PROPERTIES
• CHAPTER 4. z-EMBEDDING IN βX x βY
• CHAPTER 5. A NOTE ON δθ-REFINABLE SPACES
• CHAPTER 6. ON COUNTABLY COMPACT EXTENSIONS OF NORMAL LOCALLY COMPACT M-SPACES
• CHAPTER 7. A CHARACTERIZATION OF CONTINUOUSLY SEMIMETRIZABLE SPACES
• CHAPTER 8. DENSITY OF COMPACTIFICATIONS
• CHAPTER 9. THE PIXLEY-ROY TOPOLOGY ON SPACES OF SUBSETS
• CHAPTER 10. SEPARATING CLOSED DISCRETE COLLECTIONS OF SINGULAR CARDINALITY
• CHAPTER 11. OPEN MAPPING THEORY
• CHAPTER 12. MOORE - CLOSED AND LOCALLY MOORE - CLOSED SPACES
• CHAPTER 13. A CONSTRUCTION OF A QUASI-METRIC SOUSLIN SPACE WITH A POINT-COUNTABLE BASE
• CHAPTER 14. ON GENERATING NON-ORTHOCOMPACT SPACES
• CHAPTER 15. THE ALEXANDROFF-URYSOHN METRIZATION THEOREM REVISITED
• CHAPTER 16. THE G(m)-SPACES AND OTHER RELATED TOPICS
• CHAPTER 17. STRONG S AND L SPACES UNDER MA
• CHAPTER 18. A SELECTION-THEORETIC APPROACH TO CERTAIN EXTENSION THEOREMS
• CHAPTER 19. SOME SURPRISING BASE PROPERTIES IN TOPOLOGY II
• CHAPTER 20. SOME RESULTS FROM A-SPACES
• CHAPTER 21. SOME OBSERVATIONS ON SEMICOMPLETABLE MOORE SPACES
• CHAPTER 22. NORMALITY AND SEPARABILITY OF MOORE SPACES
• CHAPTER 23. ORTHOCOMPACTNESS IS NORMALITY IN FINITE PRODUCTS OF LOCALLY COMPACT LOTS'S
• CHAPTER 24. A REDUCTION OF THE HEREDITARILY SEPARABLE NON-LINDELÖF PROBLEM
• CHAPTER 25. FIRST COUNTABLE SPACES WITH CALIBER ϰ1 MAY OR MAY NOT BE SEPARABLE
• CHAPTER 26. SOME EXAMPLES CONCERNING α-BOUNDED SPACES
• CHAPTER 27. NON-NORMAL SPACES
• CHAPTER 28. COMPLETE MAPPINGS IN BASE OF COUNTABLE ORDER THEORY
• CHAPTER 29. LOCALLY SEPARABLE MOORE SPACES